The analytical seismic response of multi-story buildings isolated by the friction pendulum system (FPS) is investigated under near-fault motions. The superstructure is idealized as a linear shear type flexible building. The governing equations of motion of the isolated structural system are derived and the response of the system to the normal component of six recorded near-fault motions is evaluated by the step-by-step method. The variation of top floor absolute acceleration and sliding displacement of the isolated building is plotted under different system parameters such as superstructure flexibility, isolation period and friction coefficient of the FPS. The comparison of results indicated that for low values of friction coefficient there is significant sliding displacement in the FPS under near-fault motions. In addition, there also exists a particular value of the friction coefficient of FPS for which the top floor absolute acceleration of the building attains the minimum value. Further, the optimum friction coefficient of the FPS is derived for different system parameters under near-fault motions. The criterion selected for optimality is the minimization of both the top floor acceleration and the sliding displacement. The optimum friction coefficient of the FPS is found to be in the range of 0.05 to 0.15 under near-fault motions. In addition, the response of a bridge seismically isolated by the FPS is also investigated and it is found that there exists a particular value of the friction coefficient for which the pier base shear and deck acceleration attain the minimum value under near-fault motions.